Analysis of adaptive differential PCM of a stationary Gauss - Markov input

An adaptive matched differential pulse-code modulator (AMDPCM) is analyzed. The adaptation of the symmetric uniform quantizer parameter is performed by fixed multipliers assigned to the quantizer output levels. The input is stationary first-order Gauss-Markov. The correlation of the samples is used as the leakage parameter in the matched integrator, with the predictive reconstruction similarly matched. For a -level quantizer and multipliers the limiting joint distribution of the prediction error and is derived and the asymptotic sample-point and time-averaged mean-square error (rose) and mean and variance of as functions of are computed and plotted. It is found that the asymptotic performance of AMDPCM does not depend on the choice of , that the increase in mse incurred by using A(M)DPCM instead of (M)DPCM with is small, with mse(A(M)DPCM) mse ((M)DPCM) as , and that the signal-to-noise ratio of AMDPCM does not depend on the input power.